In the USA, the only person who has the right to negotiate a commission is the broker. If the agent is not the firm’s broker, I’d suggest calling said broker and explaining what happened.
No ethical broker wants unethical salespeople in their office. When the real estate commission fines a salesperson, it also fines the broker and the office–double fines.
It turns out the guy I was corresponding with is a broker - I didn’t make that distinction, because I don’t know enough about the field.
This is exactly what he said in his email to me:
It very well could be a miscommunication, that “compensate her for her time” meant negotiating her commission on the sale or something, but to my non-real-estate agent eyes, that looked like he was telling me that I had to pay Regan to take us out and show us properties.
In other, better news, I have been emailing with a different REALTOR! who has been very enthusiastic about showing us houses, and has not mentioned any payment required by us. 
That’s so weird. It’s HIS job to work out co-brokerage arrangements with agents he is cooperating with in client showings, not yours. You should have nothing to do with this. This is worked out between them, it should be transparent to you. The only scenario in which you would be “negotiating” compensation with an agent is if you were hiring a “buyer broker” agent to represent you exclusively, and even in that scenario it is usually arranged 90%+ of the time for the buyer broker to share in the total commission paid by the seller.
The only time you, (as a buyer) would normally be paying an agent directly is if you had a buyer broker and they found you an off market, unlisted deal where the seller was not willing to pay an agent commission period.